U.S. patent number 3,868,698 [Application Number 05/409,132] was granted by the patent office on 1975-02-25 for stimulation control apparatus for an ink jet recorder.
This patent grant is currently assigned to The Mead Corporation. Invention is credited to John L. Dressler.
United States Patent |
3,868,698 |
Dressler |
February 25, 1975 |
**Please see images for:
( Certificate of Correction ) ** |
STIMULATION CONTROL APPARATUS FOR AN INK JET RECORDER
Abstract
A drive circuit for a stimulation transducer suppresses
generation of satellite drops in an ink jet recorder. The drive
circuit is an oscillator which tracks the resonant frequency of the
stimulation transducer. As the resonant frequency of the transducer
changes during normal operation, the frequency of the driving
signal also changes, so that the power output of the transducer
remains essentially unchanged. This provides accurate regulation of
the filament length for the jets being stimulated and unexpectedly
also suppresses generation of satellite drops. The drive circuit
comprises an amplifier, a load resistor and positive and negative
feedback paths to the input terminals of the amplifier. The load
resistor is incorporated within the negative feedback path as well
as within the supply path for the stimulation transducer. In
general the impedance of the stimulation transducer is minimum at
the resonant frequency thereof, so that for any shifting of the
resonant frequency there is an increase in the input impedence to
the transducer. This produces a voltage variation across the load
resister which in turn alters the negative feedback to the
amplifier. Means are provided for adjusting the negative feedback
signal so as to maintain the amplifier in a state of continuous
oscillation. The frequency at which this oscillation occurs is the
frequency at which the impedance of the transducer is minimum, and
therefore the drive circuit tracks the resonant frequency of the
stimulation transducer.
Inventors: |
Dressler; John L. (Kettering,
OH) |
Assignee: |
The Mead Corporation (Dayton,
OH)
|
Family
ID: |
23619182 |
Appl.
No.: |
05/409,132 |
Filed: |
October 24, 1973 |
Current U.S.
Class: |
347/75; 318/116;
331/183; 310/317; 331/143 |
Current CPC
Class: |
B41J
2/115 (20130101) |
Current International
Class: |
B41J
2/115 (20060101); B41J 2/07 (20060101); G01d
015/18 () |
Field of
Search: |
;346/75
;331/141,110,109,183,116R,116M ;310/8.1 ;318/116,118 |
References Cited
[Referenced By]
U.S. Patent Documents
Primary Examiner: Hartary; Joseph W.
Attorney, Agent or Firm: Biebel, French & Bugg
Claims
What is claimed is:
1. Apparatus for stimulating a filament of recording fluid to break
up into uniformly sized and regularly spaced drops comprising
electically driven vibrating means having a naturally resonant
frequency near the natural frequency of said filament, an amplifier
for supplying an electrical driving signal for said vibrating
means, and positive and negative feedback means for causing
oscillation of said amplifier; said negative feedback means
comprising means for generating a negative feedback signal
corresponding to the impedance of said vibrating means and causing
oscillation of said amplifier to occur at a frequency which
minimizes said impedance.
2. Apparatus for stimulating a filament of recording liquid to
break up into a stream of uniformly sized and regularly spaced
drops comprising:
1. a transducer which responds to an oscillating electrical
operating current by producing mechanical vibrations at a common
frequency therewith, said transducer having a naturally resonant
frequency at which its impedance to said operating current is
minimum, and said naturally resonant frequency being near the
natural frequency of said filament and subject to minor shifting
during operation,
2. means mounting said transducer for vibrational stimulation of
said filament,
3. means for producing said electrical operating current and
adjusting the frequency thereof for correspondence with said
naturally resonant frequency, and
4. amplitude adjustment means for regulating the peak amplitude of
said operating current.
3. Apparatus for stimulating a filament of recording liquid to
break up into a stream of uniformly sized and regularly spaced
drops comprising:
1. a transducer which responds to an oscillating electrical
operating current by producing mechanical vibrations at a common
frequency therewith, said transducer having a naturally resonant
frequency at which its impedance to said operating current is
minimum, and said naturally resonant frequency being near the
natural frequency of said filament and subject to minor shifting
during operation,
2. means mounting said transducer for vibrational stimulation of
said filament,
3. an amplifier for producing a driving signal which drives said
operating current at a common frequency therewith,
4. a load resister connected to the input side of said transducer
so that at least a portion of said operating current passes
therethrough whereby the voltage drop across said resister varies
inversely with the electrical impedance of said transducer,
5. feedback means connected to the input side of said amplifier for
causing said driving signal and said operating current to oscillate
at a frequency which maximizes the voltage drop across said load
resister, and
6. feedback adjustment means for applying to the input side of said
amplifier an adjustment signal which regulates the peak amplitude
of said operating current.
4. Apparatus according to claim 3 said amplifier having both
positive and negative feedback terminals for connection to said
feedback means.
5. Apparatus according to claim 4 the portion of said feedback
means connected to said negative feedback terminal comprising a
path joining said negative input terminal to the input side of said
transducer.
6. Apparatus according to claim 5 further comprising a second
amplifier having its input side connected for receiving said
driving signal from the first aforesaid amplifier and its output
side connected to the side of said load resister which is remote
from said transducer, whereby said second amplifier generates said
operating current and delivers it to said load resister.
7. Apparatus according to claim 6 the portion of said feedback
means connected to said positive feedback terminal comprising a
path joining said positive feedback terminal to the input side of
said second amplifier.
8. Apparatus according to claim 7 said path joining said positive
feedback terminal comprising means for producing initial
oscillation of said driving signal at a frequency near the
naturally resonant frequency of said transducer.
9. Apparatus according to claim 7 said resistance-capacitance
network comprising wien bridge circuit.
10. Apparatus according to claim 6 said initial oscillation
producing means comprising a resistance-capacitance network.
11. Apparatus according to claim 3 said load resister having a
resistance between about 10 and 100 percent of the impedance of
said transducer when driven at said naturally resonant
frequency.
12. Apparatus according to claim 3 said load resister having a
resistance equal to about 25 percent of the impedance of said
transducer when driven at said naturally resonant frequency.
13. Apparatus according to claim 3 said feedback adjustment means
comprising a voltage peak detector for detecting peak values of
said operating current as seen at the input to said transducer and
a voltage dependent resistance responsive to said peak
detector.
14. Apparatus according to claim 13 said voltage dependent
resistance comprising a field effect transistor.
15. In a jet drop recording system comprising an orifice plate for
generating a row of filaments of recording liquid, an electrically
driven and frequency resonant transducer for launching drop
stimulating bending waves along said orifice plate and means for
charging and deflecting the drops which are generated by said
liquid filaments; driving means for driving said transducer at a
resonant frequency thereof comprising:
1. a high gain differential amplifier having positive and negative
input terminals and an output terminal,
2. a power amplifier having an input terminal and an output
terminal, said input terminal being connected to the output
terminal of said differential amplifier,
3. a load resister connected between the output terminal of said
power amplifier and an imput terminal of said transducer,
4. a first negative feedback branch comprising a feedback resister
and connected between said input terminal of said transducer and
the negative input terminal of said differential amplifier,
5. a second negative feedback branch comprising gain adjusting
means and connected between said input terminal of said transducer
and said negative input terminal of said differential amplifier,
and
6. positive feedback comprising a frequency selective resistance
capacitance network connected between the output terminal of said
differential amplifier and the positive input terminal of said
differential amplifier.
16. Apparatus according to claim 15 said resistance-capacitance
network being tuned for passage of frequencies near the resonant
frequency of said transducer and comprising adjustment means for
facilitating initial locking of said driving means to the resonant
frequency of said transducer.
Description
BACKGROUND OF THE INVENTION
This invention relates to stimulation control of an ink jet
recorder and has particular utility in connection with a multiple
jet device of a type generally as shown in Lyon et al. U.S. Pat.
No. 3,739,393. Recorders of this type comprise an orifice plate in
communication with a pressurized ink manifold, and the orifice
plate is provided with one or more rows of closely spaced orifices.
Typically such orifice plates may be about 26 centimeters long and
comprise two rows of over 600 orifices each. the orifice plate is
mechanically excited by a traveling bending wave, so that filaments
of ink passing through the orifices are stimulated to break up into
streams of uniformly sized and regularly spaced drops. Means are
provided for selective charging, deflection, and catching of the
drops, all as described in detail in the Lyon et al. patent and
other references cited therein. Such a recorder is capable of
generating and switching over 50 million drops per second for
recording of an image corresponding to stored digital data.
Typically the image will be recorded on a web traveling beneath the
print head at a speed of about 3 meters per second.
One of the problems in the operation of such a recording device is
the generation of satellite drops. These are small unwanted drops
which are formed during the liquid filament breakup process. The
phenomenom of satellite drop generation is well known in the prior
art, and apparatus for suppression thereof is shown in Stauffer
U.S. Pat. No. 3,334,351 and in the Keur et al. U.S. Pat. No.
3,683,396. However, these prior art devices deal with single jet
recorders wherein a stream of drops is generated by an elongated
nozzle arrangement. In the Stauffer patent it is proposed to
suppress satellite drops by a plural vibrator arrangement, and in
Keur et al. the suppression is accomplished by a special design
configuration for the nozzle itself. Neither of these prior art
arrangements is applicable to a multiple jet arrangement of the
type of interest herein.
One prior art device which has given some relief to the satellite
drop problem is the rotatable transducer disclosed in Houser U.S.
Pat. No. 3,701,476. This patent discloses an arrangement for
accurate adjustment of the point at which stimulation energy is
applied to the orifice plate. It has been found that by making
careful adjustment of the point of contact between a stimulating
probe and the orifice plate as disclosed by Houser, that satellite
drop generation may be greatly reduced. However, it has been found
that many satellite drops are still generated, and these drops
manifest themselves as a very fine mist which collects on the
electrical components of the print head. Over a period of time this
mist buildup causes electrical shorting problems, thereby
necessitating frequent shutdown for cleaning and imposing severe
operational restrictions on the recording system.
It has not been found that the filament length of the liquid jets
being generated by the orifice plate unexpectedly affects the
generation of satellite drops. It is well known that the filament
length is dependent upon a number of factors, including the
amplitude of the applied stimulation energy, and the satellite drop
dependence upon filament length was found during the course of
experimentation with the stimulation amplitude. It is not known
exactly how the filament length affects satellite drop formation,
but it has been observed that production of satellite drops by a
multiple jet recording head varies profoundly with only slight
changes in the level of applied stimulation energy. In general the
jets in such a head are not stimulated at the same phase, and the
only apparent direct effect of changes in the stimulation amplitude
is a fairly uniform change in the length of all jet filaments.
It has been further found in accordance with this invention that
during normal operation of a stimulation transducer there is a
variation in the resonant frequency of the transducer. While this
variation may represent a relatively small fraction of the nominal
driving frequency (which should correspond roughly with the natural
break up frequency of the liquid jets), it has a rather pronounced
effect upon the amount of stimulation energy generated by the
transducer. This in turn affects the jet filament length and hence
the amount of satellite drops which are generated. In this
connection it is to be noted that while the "resonant" frequency of
the transducer undergoes a shift, the actual stimulation frequency
does not change, because the oscillation circuit which drives the
stimulator continues to operate at a fairly constant frequency.
Therefore the principal affect of the changing resonant frequency
of the transducer is a change in the electrical impedence thereof
at the frequency of actual driving. This changing impedence changes
the amplitude of the vibrational output, thereby altering the jet
filament length and affecting the generation of satellite drops.
The impedence of the transducer is minimum at its resonant
frequency, and in general the driving voltage for the transducer is
adjusted for production of a optimum jet filament length at the
resonant condition. When the resonant frequency shifts, the jet
filaments lengthen and satellite drop production increases.
SUMMARY OF THE INVENTION
This invention reduces satellite drop generation in an ink jet
recorder by providing a stimulation drive circuit which tracks the
resonant frequency of the stimulation transducer and alters the
driving frequency in accordance therewith. Thus the stimulation
transducer is driven at its resonant frequency and its power output
remains relatively constant. This in turn regulates the length of
the ink jet filament and suppresses generation of satellite drops.
While this causes the jets to be stimulated at a frequency which
may vary slightly from the natural frequency thereof, such a small
departure does not appear to be in any way detrimental to the
operation of the recorder. However, by driving the stimulation
transducer always at its resonant frequency, the driving circuit
always sees the same output impedence and greatly improved overall
performance is achieved.
When the stimulation transducer oscillates, precisely at its
resonsant frequency (or at one of several resonant frequencies),
the impedence which is seen by the driving circuit is a local
minimum. Therefore by operating as above described, there is
achieved a further beneficial effect in that the driving circuit
may operate at a relatively low voltage level. Thus there is
avoided any requirement for high voltage circuit components and a
significant cost savings is achieved.
The circuit which is employed for driving the stimulation
transducer comprises an amplifier, a load resister, and positive
and negative feedback paths to the amplifier input. The load
resister is placed in the negative feedback path, and the input for
the stimulation transducer is taken from the output side of the
load resistor. Means are provided for adjusting the feedback so
that sustained oscillation takes place. This oscillation occurs at
the resonant frequency of the stimulation transducer because the
impedence characteristic of the transducer causes the overall loop
gain through the amplifier to be less than 1 at all other
frequencies. As the resonant frequency of the transducer shifts
there is a corresponding shift in the frequency for which
oscillation is enabled. Hence the driving circuit tracks the
resonant frequency of the transducer.
It is therefore seen that it is a primary object of this invention
to suppress the generation of satellite drops in an ink jet
recorder. Another object of this invention is to regulate the
length of the filaments of recording fluid in such a recorder.
Still another object of the invention is to track the resonant
frequency of a stimulation transducer and to adjust the oscillation
frequency of the driving circuit therefor in accordance therewith.
Other and further objects and advantages of the invention will be
apparent from the following description, the accompanying drawings
and the appended claims.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is a generalized diagram of a stimulation transducer driving
circuit in accordance with this invention;
FIG. 2 is a detailed schematic diagram of a driving circuit for a
stimulation transducer with generalized illustration of an ink jet
recording head;
FIG. 3 is a root locus plot for the circuit of FIG. 2; and
FIG. 3A is an enlargement of a portion of the plot of FIG. 3.
DESCRIPTION OF THE PREFERRED EMBODIMENT
A preferred form of the invention, as illustrated generally by FIG.
1, comprises a drive circuit 11 connected for driving control of a
stimulation transducer 12. Stimulation transducer 12 may be mounted
in an ink jet recording head 13 as illustrated generally in FIG. 2.
Thus recording head 13 may comprise an ink manifold 14, an orifice
plate 15, a charge ring plate 16, a pair of deflection electrodes
17, and a catcher 18. A supply of ink 21 is maintained under
pressure in manifold 14 and exits through orifice 14 via a series
of orifices 22 (only one orifice 22 being illustrated) to form a
series of filaments 23. As described in detail in Lyon et al. U.S.
Pat. No. 3,739,393 and in Houser U.S. Pat. No. 3,701,476,
stimulator 12 may have a probe which reaches downwardly for contact
with orifice plate 15. Vertical oscillation of the probe generates
an oscillating disturbance at one end of orifice plate 15, and
these oscillations travel the length of orifice plate 15 thereby
causing filaments 23 to break up uniformly into drops 24. In
accordance with the practice of this invention the drops 24 are
generated without concomitant generation of an excessive number of
satellite drops (not illustrated).
Continuing with the description of recording head 13, it will be
seen that some of drops 24 deposit on a moving web 20 while other
of drops 24 are deflected into a catcher 18. Selective catching of
drops 24 is accomplished by selective application of charge contol
signals to a series of charge rings 19 in charge ring plate 16. An
electrical filed is established between deflection electrodes 17,
and those of drops 24 which are charged by charge rings 19 (each
jet has its own charge ring) are deflected by the electrical field
into catcher 18. As shown by the Lyon and Houser patents, there may
be two rows of jets and two catchers with each catcher having a
face which serves as one deflection electrode for an associated row
of streams.
The construction details of transducer 12 are described in the
above mentioned Houser patent wherein it is shown that the primary
element may be a piezoelectric crystal which converts an electrical
input signal to an output oscillation. This output oscillation is
coupled through a load mass and a horn structure to the above
mentioned probe for application to orifice plate 15. In general
these transducers may have several resonant frequencies, one of
which should correspond closely with the natural frequency of
streams 23. Drive circuit 11 is designed to drive transducer 12 at
the correct resonant frequency and to track that frequency as it
changes normally due to heating or other causes during routine
operation of the recording system.
In preferred embodiment transducer drive circuit 11 comprises a
differential amplifier 30, a power amplifier 31, a load resistor
32, and negative and positive feedback loops to the negative and
positive input terminals 34 and 42 of differential amplifier 30. It
is not necessary that amplifier 30 be a differential amplifier, so
long as summing junctions be provided for negative and positive
feedback loops. Further it will be appreciated that power amplifier
31 is not an essential element of the invention and is merely
employed for current amplification without voltage gain. It is,
however, important that the negative feedback loop be connected to
the output side of load resistor 32 and that the positive feedback
loop be connected so as to exclude load resistor 32 therefrom.
As illustrated in FIG. 1, the above mentioned negative feedback
loop extends from output terminal 53 of differential amplifier 30
back around to the negative input terminal 34. The negative
feedback loop therefore includes load resistor 32 and branches out
into two branches at the output side thereof. One of these two
negative branches includes only a resister 33 whereas the other
branch comprises a peak detector 35, a differential amplifier 36
and a voltage dependent resistance 37. The positive feedback loop
extends from output terminal 53 of amplifier 30 back through an R-C
network to the positive input terminal 42. In general the gain
across amplifier 30 is extremely high, but the only signal
amplified is a very small difference signal which results when the
positive and negative feedback signals are combined. Therefore in
computing the overall loop gain around the loop including the
positive feedback path, account must be taken of the substractive
effect of the negative feedback loop. For making circuit 11 deliver
a steady state oscillating drive signal to transducer 12, it is
necessary that the loop gain around the positive loop be exactly
equal to 1.0, and resistor 33 is selected for production of this
gain condition.
For reasons which are discussed below the oscillation of driving
circuit 11 occurs at a frequency which closely matches the resonant
frequency of transducer 12. In the special case of a transducer
having only one resonant frequency, the above mentioned positive
feedback loop may comprise a simple connection from the output of
amplifier 30 back around to the positive terminal of amplifier 30.
In general, however, transducer 12 will have several resonant
frequencies, and it is desired to drive transducer 12 at that one
of its resonant frequencies which most nearly approximates the
natural frequency of the liquid filaments 23. Accordingly the
positive feedback loop around amplifier 30 comprises an R-C network
designed to produce oscillation of amplifier 30 at a frequency near
that one of the resonant frequencies of transducer 12 which it is
desired to track. Thus as illustrated in FIG. 1, the positive
feedback loop comprises resisters 38 and 39 and capacitors 40 and
41 connected in a wien bridge arrangement. The bridge arrangement
has an attenuation of approximately 3 (or gain of one third) at the
desired tracking frequency, and therefore the negative feedback
loop (comprising two branches as above described) is designed to
produce an effective gain of three across amplifier 30 from input
terminal 42 to output terminal 53. Thus the overall gain around the
loop including the positive feedback path is 1.0 at the tracking
frequency.
The frequency tracking operation of drive circuit 11 occurs,
because of the inclusion of load resistor 32 in the above mentioned
negative feedback path and the connection of the input terminal of
transducer 12 to the output side of resister 32. This arrangement
causes resister 32 and transducer 12 to behave like a voltage
divider, and since the voltage drop across transducer 12 is
frequency dependent, the same is likewise true of the voltage drop
across resistor 32. Then because of the feedback connection to
negative input terminal 34, it may be seen that there is a
frequency dependent gain condition wherein the effective gain
around the loop including the positive feedback path is maximum at
the frequency for which the voltage drop across resistor 32 is also
maximum.
The frequency at which the voltage drop across resistor 32 is
maximum necessarily must be the frequency at which the impedence of
transducer 12 and the voltage drop thereacross are minimum. The
frequency for which this occurs is the resonant frequency of the
transducer, and hence for this frequency the conditions are such as
to promote a maximum growth rate for any noise induced
disturbances. The negative feedback branch through peak detector
35, amplifier 36, and voltage dependent resistance 37, continually
adjusts the system gain to maintain a stable oscillation condition
at whatever frequency the oscillations may be occurring. What this
means is that the loop gain becomes 1.0 for the above mentioned
resonant frequency and less than 1.0 for all other frequencies. It
follows that amplifier 30 and drive circuit 11 can oscillate only
at a frequency corresponding to a resonant frequency of transducer
12.
The above mentioned gain adjustment occurs because peak detector 35
continually monitors the peak value of the sinusoidal voltage
appearing at the output side of resistor 32 and supplies a
corresponding control signal through amplifier 36 to voltage
dependent resistance 37. Amplifier 36 applies a negative voltage to
voltage dependent resistance 37, and the magnitude of this voltage
increases (i.e., increases in the negative direction) whenever the
sinusoidal signal at the output side of resister 32 begins growing
in amplitude. This then causes an increase in the resistance of
resistance network 37 as well as an increase in the voltage drop
thereacross. The increased voltage drop across resistance network
37 increases tht negative feedback applied to terminal 34, thereby
decreasing the amplitude of the circuit oscillation. In this
respect, therefore, the gain adjusting means operates in a manner
analogous to the operation of a tungsten filament lamp or other
similar device frequently employed in prior art oscillation
networks. In this case, however, the oscillation frequency of the
circuit undergoes a controlled change, whereas the gain adjustment
means of the usual oscillator enables sustain oscillation at a non
changing frequency.
As described above, load resistor 32 performs a necessary function
in the operation of the invention in facilitating the tracking of
the resonant frequency of transducer 12. In general drive circuit
11 locks in more easily to the resonant frequency of transducer 12
when load resister 32 has a relatively large resistance. However,
resistive heating across resister 32 causes a power loss, and
therefore there is an optimum resistance value for resister 32.
Preferably the resistance of resister 32 should be selected in
accordance with the impedence of transducer 12 as measured at the
resonant frequency (at which frequency the impedence is almost
entirely resistive).
Experience with drive circuits such as drive circuit 11 has shown
that resister 32 preferably should have a resistance of at least
about 10 percent of the resistance of the transducer 12, with a
resistance ratio of about 25 percent being optimum. From a power
disipation point of view resister 32 preferably should not have a
resistance greater than the resistive impedence of transducer 12 as
measured at the resonant frequency thereof. In a typical case the
resonant frequency which is being tracked is about 50 KHz, and when
in resonance at this frequency transducer 12 may have an internal
impedence of about 200 ohms. Under such conditions a resistance of
about 47 ohms for resister 32 has been found to be highly
satisfactory.
A schematic diagram of drive circuit 11 is shown in FIG. 2. As
shown therein power amplifier 31 comprises 2 transistors 43 and 44
connected in a push-pull arrangement. Amplifier 31 has a voltage
gain of 1 and serves as a low output impedence of differential
amplifier 30. Voltage dependent resistance 37 comprises a resister
45 in series with a field effect transistor 46. The gate voltage of
transistor 46 varies with the output of amplifier 36, and this in
turn varies the resistance between the drain and the source
terminals of the transistor. As a consequence thereof, the negative
feedback applied to terminal 34 of differential amplifier 30
follows the voltage peaks detected by the peak detector 35.
Peak detector 35 comprises a diode 47, a pair of resisters 48 and
49, and a capacitor 50 connected as illustrated to the negative
input terminal of amplifier 36, which it may be noted is preferably
a high gain differential amplifier. The reference voltage which is
applied to the positive input terminal of amplifier 36 is generated
by a tapped resister 52 in parallel with a zener diode 51 and
sources of positive and negative potential (typically about 12
volts) all connected as illustrated.
As described previously the network connected to the positive input
terminal 42 of differential amplifier 30 is designed to maintain
amplifier oscillation at a frequency near a specified resonant
frequency of transducer 12. For a typical resonant frequency of
about 50 kilohertz resisters 38 and 39 may each have a resistance
of about 1,600 ohms and capacitors 40 and 41 may each have a
capacitance of about 2,000 micro-microfarads. Further as
illustrated in FIG. 2, resisters 38 and 39 may comprise ganged
variable resistive elements 38' and 39' for simultaneous
adjustment. The ganged variable resistive elements 38' and 39' are
provided to facilitate initial frequency lock at the desired
resonance frequency of transducer 12. This initial frequency lock
may be achieved by adjusting resistive components 38' and 39' and
observing the frequency of system oscillation. The oscillation
frequency will change with the changing adjustment of resistive
component 38' and 39' until frequency lock with transducer 12 has
been achieved. At this point further adjustment of the ganged
resistive components will produce no further change in the system
oscillation frequency.
As further illustrated in FIG. 2, resister 33 is also variable.
Preferably resister 33 is a 50,000 ohm potentiometer which may be
used to bias FET 46 in the proper operating region. When resister
33 is adjusted to the correct value, the amplitude of the driving
voltage to transducer 12 can be adjusted in a range anywhere from
about 0 volts to about 20 volts peak to peak. Adjustment of the
amplitude of the transducer driving voltage is effected by
adjusting the position of the tap on resistor 52.
A root locus plot for the circuit of FIG. 2 is presented in FIGS. 3
and 3A. The expression for which this plot is made has the general
form:
KG(s)/[ 1-KG(s)]
where:
K=(R.sub.37 + R.sub.33)/R.sub.37
and ##SPC1##
Z is the transfer function for transducer 12 which in a typical
case has been found to be given approximately by the equation:
##SPC2##
When the system is oscillating the resistance of voltage dependent
resistance 37 (and thus also K) is adjusted for a stable condition.
This stable oscillation condition corresponds to the point at which
two of the poles 60 and 61 cross the real axis 62 of FIGS. 3 and
3A. As shown in FIG. 3 and more particularly in enlarged form in
FIG. 3A, the axis crossing occurs when K has a value of about 2.52
to produce system oscillation at a frequency of 3.158 .times.
10.sup.5 radians per sec. or about 50 KHz. It is noted that the
poles which cross the real axis at this gain are poles which for a
gain of zero have a real part of -250 and an imaginary part of
3.157 .times. 10.sup.5. These poles are produced by the zeros of
transducer 12. The plot, therefore, confirms that it is the low
impedence resonance of transducer 12 which controls the frequency
of system oscillation.
While the form of apparatus herein described constitutes a
preferred embodiment of the invention, it is to be understood that
the invention is not limited to this precise form of apparatus, and
that changes may be made therein without departing from the scope
of the invention.
* * * * *